Kirchhoff's Laws of Radiation (idea)

Gustav Robert Kirchhoff's contribution to our understanding of how light and matter
interact is his set of three laws of radiation. They predict what sort of spectrum
an object will emit based upon the physical properties of the object.
Kirchhoff devised these laws in the latter half of the nineteenth century,
prior to our understanding of atomic physics and quantum mechanics, but
on a macroscopic level they describe the interaction of matter and
radiation quite well. The laws are as follows:

A continuous spectrum passed through a cool, thin gas will result in
a continuum spectrum with breaks at the same wavelengths as the emission
lines described in the Second Law -- an absorption line spectrum.

These three laws embody much of the fundamental physics of radiation and
radiative transfer. The first is a simplified explanation of black body
radiation, namely that any dense object will emit a characteristic,
continuous spectrum. It was later determined that the shape and intensity
of this spectrum is only a function of the object's temperature, and
nothing else, but from a purely phenomenological standpoint, the first law
is a good descriptor of black bodies. In particular, it makes no
qualifications as to the properties of the object -- it could be a metal
rod in a fire, it could be a jar full of mercury, or an incredibly dense
sphere of gas. All that matters is that it is dense. More accurately,
we now say it is "optically thick"(*) rather than dense, but Kirchhoff's
description is good enough.

The second and third laws also cover a large swath of physics, that of
emission and absorption processes by atoms in a gas or plasma. The second
law says that a thin ("optically thin"), hot gas will have an emission line
spectrum; the third law states that a cool gas will behave the opposite way,
and exhibit absorption lines. As the theory behind atomic structure and
quantum mechanics grew during the late nineteenth century, Kirchhoff and
others (notably Robert Bunsen) realized that each
element has its own unique signature of
emission and absorption lines, governed by its electron configuration. The
lines are generated by electrons emitting and absorbing energy by shifting
their position within the electronic structure of a given atom.

All atoms of a
given element exhibit the same set of lines. This is important,
because it means that hydrogen atoms (and all other elements) behave the
same way on the Sun as they do here on Earth.
In this way, we can apply our knowledge of gases here on Earth to what we
see elsewhere in the universe, and use light as a way to study the physical
properties of distant objects. This is precisely what Kirchhoff and others
did in their studies of the Sun -- by comparing the
absorption lines in the
solar spectrum to those of gases here on Earth, they found the Sun's
photosphere is composed of elements like hydrogen, helium, calcium,
iron, and nearly every other element we see here on Earth.

(*) The optical depth of a
material is defined as the ability a photon to pass through it without
being scattered or absorbed. A material with an optical depth
τ of exactly one is one in which the intensity of light passing through
it will be reduced by a factor of e. Mathematically, this is

Thus, when the optical depth becomes large, the amount of light which passes
through is very small. Physically, it indicates that the mean free path of
a photon is shorter than the thickness of the material itself.